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Conservative domain decomposition schemes for solving two-dimensional heat equations

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Abstract

In this paper, by combining the operator splitting technique, a new mass-conserved domain decomposition method for two-dimensional heat equations is proposed. Along the each direction, the interface fluxes are first calculated from the explicit fluxes, then the sub-domain’s interior solutions are paralelly computed by the C–N implicit scheme. The scheme is stable under the condition \(r\le 2(\sqrt{6}-2)\) and the corresponding convergence order of the scheme are given in \(L^2\)-norm. Numerical results confirm the theoretical results.

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Acknowledgements

This work was supported by Natural Science Foundation of China (Grant Nos. 6170325, 61503227), and Natural Science Foundation of Shandong Government (Grant Nos. ZR2017BA029, ZR2017BF002), Shandong Agricultural University (Grant No. xxxy201704), and National natural science foundation funding project application for key subject.

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Authors and Affiliations

  1. School of Information Science and Engineering, Shandong Agricultural University, Taian, 271018, Shandong, China

    Zhongguo Zhou & Lin Li

  2. School of Resources and Environment, Shandong Agricultural University, Taian, 271018, Shandong, China

    Zhongguo Zhou

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  1. Zhongguo Zhou
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  2. Lin Li
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Correspondence to Zhongguo Zhou.

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Communicated by Frederic Valentin.

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Zhou, Z., Li, L. Conservative domain decomposition schemes for solving two-dimensional heat equations. Comp. Appl. Math. 38, 1 (2019). https://doi.org/10.1007/s40314-019-0767-y

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  • DOI: https://doi.org/10.1007/s40314-019-0767-y

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